Trigonometric Identities
Identities are the equations, which are true for any value of a variable. We have 3 different types of trigonometric identities i.e. Pythagorean identity, reciprocal identity, and quotient identity.
Pythagorean Identity
At this level, we only have 3 Pythagorean identities in our syllabus. The proof of them is not significant to us. Below is the list showing the trigonometric identities.
- cos2A + sin2A = 1
- 1 + tan2A = sec2A
- 1 + cot2A = cosec2A
Reciprocal Identity
If observed carefully, then, we can find that many trigonometric ratios are just the reverse of each other. We have 3 reciprocal identities listed below:
- sec θ = 1/cos θ
- cosec θ = 1/sin θ
- cot θ = 1/tan θ
Quotient Identity
tan θ and cot θ can be rewritten in terms of sinθ and cosθ.
- tanθ = sinθ/cosθ,
- cotθ = cosθ/sinθ
Example: Prove that,
Solution:
From Trigonometric Identity,
1 + tan2A = sec2A, and
1 + cot2A = cosec2A
Hence, the equation can be rewritten as,
Also, secA = 1/cosA, cosecA = 1/sinA,
⇒ LHS = tan2A
Hence, L.H.S. = R.H.S.
Also, Read
Introduction to Trigonometry Class 10 Maths Notes Chapter 8
CBSE Class 10 Maths Notes Chapter 8 Introduction to Trigonometry are an excellent resource, for knowing all the concepts of a particular chapter in a crisp, and friendly manner. Our articles, help students learn in their language, with proper images, and solved examples for better understanding the concepts.
Chapter 8 of the NCERT Class 10 Maths textbook delves into the world of Introduction to Trigonometry used in real life and covers various topics such as what is trigonometry, fundamentals of trigonometric ratios like sine, cosine, secant, tangent, cosecant, cotangent, and identities. These notes are designed to provide students with a comprehensive summary of the entire chapter and include all the essential topics, formulae, and concepts needed to succeed in their exams.